There were 4 clips and two of them definitely seemed to star Robert Wilson from I Beheld His Glory (1952), but the other two I couldn't quite work out. The question of the identity of the actor/film of the 2nd and 4th clips in this link has bugged me for almost a year.
I'd also heard of a film called the Living Bible, which I'd not really been that interested in and assumed was a 70s tie in with the translation / paraphrase of the same name. Nevertheless, it came up cheap on eBay the other day so I bid for it.
It turns out that what was actually on the discs was something called The Living Christ series, and this was indeed the film used in the spoofs above. It would appear that the 12 half hour episodes started being released individually 1951 as films shown to church youth groups. The films were made by Catholic film company "Cathedral Films", and became so successful that they created two film spin offs, I Beheld His Glory in 1952, and Day of Triumph in 1954, although the IMDB lists both films as being 1953.

I am surprised that neither Campbell and Pitts's "The Bible on Film" nor Kinnard & Davis's "Divine Images" seem to mention this series.
Matt
N.B. - This post was back-dated to when much of it was first noted down in a discussion at the Arts and Faith discussion forum